Independence number of intersection graphs of axis-parallel segments

05/30/2022

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by   Marco Caoduro, et al.

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We prove that for any triangle-free intersection graph of n axis-parallel segments in the plane, the independence number α of this graph is at least α≥ n/4 + Ω(√(n)). We complement this with a construction of a graph in this class satisfying α≤ n/4 + c √(n) for an absolute constant c, which demonstrates the optimality of our result.